Question

Solve each equation (Isolating first)

Answer 1

$3 \times {( \frac{1}{8} )}^{2x} = 12 \\ \Leftrightarrow {( \frac{1}{8} )}^{2x} = 4 \\ \Leftrightarrow {( {2}^{ - 3}) }^{2x} = {2}^{2} \\ \Leftrightarrow {2}^{ - 6x} = {2}^{2} \\ \Leftrightarrow - 6x = 2 \\ \Leftrightarrow x = - \frac{1}{3} \\ \\ 2 {\sqrt[3]{5}}^{4x} = 50 \\ \Leftrightarrow { \sqrt[3]{5} }^{4x} = 25 \\ \Leftrightarrow {5}^{ \frac{4x}{3} } = {5}^{2} \\ \Leftrightarrow \frac{4x}{3} = 2 \\ \Leftrightarrow 4x = 6 \\ \Leftrightarrow x = \frac{3}{2}$

Answer 2

Answer to Q1:

x= -1/3

Step-by-step explanation:

We have given the equations.

We have to solve these equations.

The first equation is :

$3.(\frac{1}{8})^{2x}$

$(\frac{1}{8})^{2x}=4$

$(2^{-3x})^{2x}=4$

$2^{-6x}=4$

$2^{-6x}=2^{2}$

As we know that bases are same then exponents are equal.

-6x = 2

x = 2/-6

x=-1/3

Answer to Q2:

x = 3/2

Step-by-step explanation:

The given equation is :

$2.\sqrt[3]{5}^{4x}=50$

We have to find the value of x.

First,we multiply both sides of equation by 1/2 we get,

$5^{4x/3}=25$

$5^{4x/3}=5^{2}$

4x/3=2

4x = 6

x = 3/2